A Formulation for Updating Finite Element
Models Through Consistent Use of Laser
Vibrometer Data

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Abstract

This thesis suggests a formulation for updating physically
meaningful parameters in analytical finite element(FE)
models using scanning laser Doppler vibrometer(SLDV) dynamic
response data. The update formulation is demonstrated in
several computer simulations.
The formulation is the result of incorporating an analytical
FE model into an experimental model. The experimental model
efficiently utilizes SLDV data to fully exploit the
instrument's capability to automatically make measurements
at many locations. The data in the experimental model is
posed in a manner consistent with an analytical FE model's
representation for harmonic response, simplifying
comparison between the two. The experimental model, which
uses finite element shape functions as a basis for a least
squares fit to the data, can be solved to give a velocity
field based only on that data. The function resulting from
inserting the analytical model into the experimental model
is an expression of the prediction error of the FE model as
compared to the test data. This function is minimized using
a quasi-Newton optimization routine, reducing the error and
resulting in an updated model.
Computer simulations of the update algorithm indicate that:
1. Analytically supplied derivatives and variable scaling
are required by the optimization routine to consistently
converge,
2. The percentage error of updated parameters falls within
two standard deviations of the data's percentage error,
3. Error in the position of the laser results in the update
algorithm's failure, and,
4. Error in the parameters not included in the update will
appear as error in the updated parameters' solution.